Looking for A/C advice

I've read on here that some of you run your generator while traveling to keep your "houses" cool. My house is pretty small, but I am in the heat of Montana, Idaho, and Eastern Washington. I've noticed my small Class C is struggling up hills with the cab A/C on high. If I run my generator for the house A/C would that take some off the work off the engine? Edit: or will that just sucks lots of gas?